非线性波方程准确孤立波解的符号计算

Exact Solitary Wave Solutions for Nonlinear Wave Equations Using Symbolic Computation

该文将机械化数学方法应用于偏微分方程领域，建立了构造一类非线性发展方程孤立波解的一种统一算法，并在计算机数学系统上加以实现，推导出了一批非线性发展方程的精确孤立波解．算法的基本原理是利用非线性发展方程孤立波解的局部性特点，将孤立波表示为双曲正切函数的多项式．从而将非线性发展方程（组）的求解问题转化为非线性代数方程组的求解问题．利用吴文俊消元法在计算机代数系统上求解非线性代数方程组，最终获得非线性发展方程（组）的准确孤立波解.

In this paper the Mathematics-Mechanization method is applied the field of differential equations. A unifying algorithm for constructing solitary wave solutions for a class of nonlinear evolution equations are given, and implemented in a.computer algebraic system.Exact solitary wave solutions of a great deal of nonlinear equations are obtained. The algorithm is based on the fact that the solitary wave solutions are essentially of a localized nature. Seeking solitary wave solutions which are in terms of hyperbolic tangent function gives a nonlinear system of algebraic equations. The system is solved by using Wu Elimination and the exact solutions of nonlinear evolution equation(s) are then obtained.